MAVI 17, Bochum 2011
THE THEORY OF CONCEPTUAL CHANGE AS A
THEORY FOR CHANGING CONCEPTIONS
Peter Liljedahl
• MAVI 2009, MAVI 2006*, CERME 2009, PME 2006*
• changes in beliefs as conceptual change
• CERME 2007*, PME 2007*, JMTE 13 (5)
• changing conceptions
• WoMB 2010
• NOMAD 16(1-2)
* with Bettina Rösken & Katrin Rolka
Origins
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• research on changes in beliefs
Teachers’ Beliefs
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beliefs ↔ practice
↕
contemporary notions
of good practice
Teachers’ Beliefs
MAVI 17, Bochum 2011
beliefs ↔ practice
↕
contemporary notions
of good practice
Teachers’ Beliefs
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beliefs ↔ practice
Beliefs are Difficult to Change
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Beliefs are “like possessions. They are like
old clothes; once acquired and worn for
awhile, they become comfortable. It does not
make any difference if the clothes are out of
style or ragged. Letting go is painful and new
clothes require adjustment” (SchommerAikins, 2004, p. 22).
Beliefs are Difficult to Change
MAVI 17, Bochum 2011
Beliefs are “like possessions. They are like
old clothes; once acquired and worn for
awhile, they become comfortable. It does not
make any difference if the clothes are out of
style or ragged. Letting go is painful and new
clothes require adjustment” (SchommerAikins, 2004, p. 22).
Beliefs are Difficult to Change
MAVI 17, Bochum 2011
Beliefs are “like possessions. They are like
old clothes; once acquired and worn for
awhile, they become comfortable. It does not
make any difference if the clothes are out of
style or ragged. Letting go is painful and new
clothes require adjustment” (SchommerAikins, 2004, p. 22).
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Changing Beliefs
Changing Beliefs
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CONCEPTUAL CHANGE
• emerges out of Kuhn's (1970) interpretation
of changes in scientific understanding
through history
• progress in scientific understanding is marked
more by theory replacement than theory
evolution
Changing Beliefs
MAVI 17, Bochum 2011
CONCEPTUAL CHANGE
• emerges out of Kuhn's (1970) interpretation
of changes in scientific understanding
through history
• progress in scientific understanding is marked
more by theory replacement than theory
evolution
Changing Beliefs
MAVI 17, Bochum 2011
CONCEPTUAL CHANGE
• emerges out of Kuhn's (1970) interpretation
of changes in scientific understanding
through history
• progress in scientific understanding is marked
more by theory replacement than theory
evolution
Replacing Conceptions
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CONCEPTUAL CHANGE
• applicable only in those instances where
misconceptions are formed through lived
experiences and in the absence of formal
instruction
Replacing Conceptions
MAVI 17, Bochum 2011
CONCEPTUAL CHANGE
• applicable only in those instances where
misconceptions are formed through lived
experiences and in the absence of formal
instruction
• phenomenon of theory rejection
cognitive
• phenomenon of theory replacement conflict
Replacing Conceptions
MAVI 17, Bochum 2011
CONCEPTUAL CHANGE
• applicable only in those instances where
misconceptions are formed through lived
experiences and in the absence of formal
instruction
• phenomenon of theory rejection
cognitive
• phenomenon of theory replacement conflict
• synthetic model
Replacing Conceptions
MAVI 17, Bochum 2011
CONCEPTUAL CHANGE
• applicable only in those instances where
misconceptions are formed through lived
experiences and in the absence of formal
instruction
• phenomenon of theory rejection
cognitive
• phenomenon of theory replacement conflict
• synthetic model
Replacing Conceptions
MAVI 17, Bochum 2011
CONCEPTUAL CHANGE
• applicable only in those instances where
misconceptions are formed through lived
experiences and in the absence of formal
instruction
• phenomenon of theory rejection
cognitive
• phenomenon of theory replacement conflict
• synthetic model
CAN I DO THIS?
Replacing Conceptions
MAVI 17, Bochum 2011
CONCEPTUAL CHANGE
• applicable only in those instances where
misconceptions are formed through lived
experiences and in the absence of formal
instruction
• phenomenon of theory rejection
cognitive
• phenomenon of theory replacement conflict
• synthetic model
CAN I DO THIS?
Hmmm ...
MAVI 17, Bochum 2011
• the theory of conceptual change is a theory of
learning and NOT a theory of teaching
Hmmm ...
MAVI 17, Bochum 2011
• the theory of conceptual change is a theory of
learning and NOT a theory of teaching
• there are NO theories of teaching
While theory provides us with lenses for analysing
learning (Lerman, 2001), the big theories do not
seem to offer clear insights to teaching and ways
in which teaching addresses the promotion of
mathematics learning. (Jaworski, 2006, p. 188)
Hmmm ...
MAVI 17, Bochum 2011
• the theory of conceptual change is a theory of
learning and NOT a theory of teaching
• there are NO theories of teaching
While theory provides us with lenses for analysing
learning (Lerman, 2001), the big theories do not
seem to offer clear insights to teaching and ways
in which teaching addresses the promotion of
mathematics learning. (Jaworski, 2006, p. 188)
IS THIS TRUE?
Hmmm ...
MAVI 17, Bochum 2011
• the theory of conceptual change is a theory of
learning and NOT a theory of teaching
• there are NO theories of teaching
Hmmm ...
MAVI 17, Bochum 2011
• I propose that the source of this tension between
theories of learning and theories of teaching is the
assumption that theories should play the same role in
teaching as they do in learning
Hmmm ...
MAVI 17, Bochum 2011
• I propose that the source of this tension between
theories of learning and theories of teaching is the
assumption that theories should play the same role in
teaching as they do in learning
• teaching and learning are inherently different
activities
IN WHAT WAYS?
Hmmm ...
MAVI 17, Bochum 2011
• I propose that the source of this tension between
theories of learning and theories of teaching is the
assumption that theories should play the same role in
teaching as they do in learning
• teaching and learning are inherently different
activities
Hmmm ...
MAVI 17, Bochum 2011
• I propose that the source of this tension between
theories of learning and theories of teaching is the
assumption that theories should play the same role in
teaching as they do in learning
• teaching and learning are inherently different
activities
• to theorize about them requires, not (necessarily) the
use of different theories, but the use of theories
differently
↓
THEORY FOR CHANGING CONCEPTIONS
Theories of → Theories for
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THEORIES OF CONCEPTUAL CHANGE
model of → model for
• Streefland (1993)
pre-image → post-image
• Simon (1995)
teaching with constructivism
• Fried (2011)
theory of / theory for / theory in
Theories of → Theories for
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NOT A NEW IDEA
• Van den Heuvel-Panhuizen (2003)
•
•
•
•
•
•
0 - 23 years, average of 8.7 years
8 males, 6 females
6 had undergraduate degrees in mathematics
7 had a degree in one of the sciences
1 had a degree in history
majority of the group had been teaching mathematics
either exclusively or in conjunction with some other
subject areas for the majority of their careers
• ALL of the participants considered themselves to be
mathematics teachers
Methodology – participants
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14 inservice secondary mathematics teachers
Methodology - interventions
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6 interventions – cognitive conflict
• the nature of mathematics
• the nature of mathematics teaching
• the nature of assessment
• the nature of student knowledge
• the nature of student learning
• the nature of student motivation
Methodology - interventions
MAVI 17, Bochum 2011
6 interventions – cognitive conflict
• the nature of mathematics
• the nature of mathematics teaching
• the nature of assessment
• the nature of student knowledge
• the nature of student learning
• the nature of student motivation
Methodology - interventions
MAVI 17, Bochum 2011
6 interventions – cognitive conflict
• the nature of mathematics
• the nature of mathematics teaching
• the nature of assessment
• the nature of student knowledge
• the nature of student learning
• the nature of student motivation
field notes
students’ journals
informal interviews
students’ essays
Methodology - data
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1.
2.
3.
4.
A musician wakes from a terrible nightmare. In his
dream he finds himself in a society where music
education has been made mandatory. “We are
helping our students become more competitive in an
increasingly sound-filled world.” Educators, school
systems, and the state are put in charge of this vital
project. Studies are commissioned, committees are
formed, and decisions are made— all without the
advice or participation of a single working musician or
composer.
The Nature of Mathematics - treatment
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Lockhart’s Lament (2008)
Grant:
Interviewer:
Grant:
Interviewer:
Grant:
Interviewer:
Grant:
A few weeks ago I had you read Lockhart's Lament in class.
Tell me what you thought about that.
It made things pretty clear, didn't it?[laughs] I mean, the way
that he described music and art sure made you think about
what we are doing to kids in math.
And?
And we sure as hell shouldn't be doing it?
So, what should we be doing?
I'm not sure. Problem solving for sure. And probably more
group work. But I haven't figured it all out yet.
So, what made you come away from your initial ideas about
mathematics?
To be honest, I had never really thought about it before ... I
hadn't really looked at what I was teaching in such a stark way.
Lockhart paints a picture that is hard to ignore.
The Nature of Mathematics - results
MAVI 17, Bochum 2011
Interviewer:
Grant:
Interviewer:
Grant:
Interviewer:
Grant:
Interviewer:
Grant:
A few weeks ago I had you read Lockhart's Lament in class.
Tell me what you thought about that.
It made things pretty clear, didn't it?[laughs] I mean, the way
that he described music and art sure made you think about
what we are doing to kids in math.
And?
And we sure as hell shouldn't be doing it?
So, what should we be doing?
I'm not sure. Problem solving for sure. And probably more
group work. But I haven't figured it all out yet.
So, what made you come away from your initial ideas about
mathematics?
To be honest, I had never really thought about it before ... I
hadn't really looked at what I was teaching in such a stark way.
Lockhart paints a picture that is hard to ignore.
The Nature of Mathematics - results
MAVI 17, Bochum 2011
Interviewer:
It can be said that when we read a book we
read ourselves into the text. In what ways do
you read yourself into Boaler's book? Speak
about your own teaching practice (past,
present, and future) in relation to the book.
The Nature of M. Teaching - treatment
MAVI 17, Bochum 2011
Experiencing School Mathematics (Boaler, 2002).
The Nature of M. Teaching - results
MAVI 17, Bochum 2011
• It was as though I was looking at my own teaching.
• I couldn't help but think that Boaler was describing my
classroom.
• Nicholas:
I certainly would fit in well with the teachers at
Amber Hill, especially with the focus on testing. But
I'm not exactly the same. I tend to make more use
of group work especially during project work.
• Chad:
It was good ... it was eye-opening. As I was
reading it I kept trying to identify myself with Jim at
Phoenix Park but I kept coming back to Amber Hill.
It was really troubling when I finally realized that I
was an Amber Hill teacher.
The Nature of M. Teaching - results
MAVI 17, Bochum 2011
• It was as though I was looking at my own teaching.
• I couldn't help but think that Boaler was describing my
classroom.
• Nicholas:
I certainly would fit in well with the teachers at
Amber Hill, especially with the focus on testing. But
I'm not exactly the same. I tend to make more use
of group work especially during project work.
• Chad:
It was good ... it was eye-opening. As I was
reading it I kept trying to identify myself with Jim at
Phoenix Park but I kept coming back to Amber Hill.
It was really troubling when I finally realized that I
was an Amber Hill teacher.
The Nature of M. Teaching - results
MAVI 17, Bochum 2011
• If the students are not going remember the
stuff we teach them then have they really
learned? And if not, then what was the point
in the first place? (Ingrid)
• If the students are not engaging with the
lesson then there is no way that they can
learn. (Eric).
• Math needs to be fun. Sitting in rows and
listening to the teacher is not fun. (Alicia).
The Nature of M. Teaching - results
MAVI 17, Bochum 2011
• If the students are not going remember the
stuff we teach them then have they really
learned? And if not, then what was the point
in the first place? (Ingrid)
• If the students are not engaging with the
lesson then there is no way that they can
learn. (Eric).
• Math needs to be fun. Sitting in rows and
listening to the teacher is not fun. (Alicia).
Conclusions
MAVI 17, Bochum 2011
1. the theory of conceptual change is a viable theory for designing
interventions for the purpose of changing conceptions
2. implementation of these interventions resulted in cognitive
conflict and eventually rejection of the participants’ a priori
beliefs
3. the cognitive conflict that precipitates this belief rejection
seems to be greatly affected by the starkness of the images
presented – especially when those images are both troubling
and undeniably reflective of the participant's practice
4. the data is replete with evidence that the participants not only
rejected beliefs pertaining to their current practices, but that
often they did so without an immediate replacement at hand
MAVI 17, Bochum 2011
THANK YOU!
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